Resources

Online Books

• The Not So Short Introduction to Latex2ε. Short introduction to Latex by Tobias Oetiker, Hubert Partl, Irene Hyna and Elisabeth Schlegl. This is the best guide to LaTex ever written.
• Handbook of Applied Cryptography. Full online version of a printed book on applied cryptography, generously made freely available by its authors Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone, and the publishers CRC Press.
• Lecture Notes on Cryptography. Lecture notes from courses given by Bellare and Goldwasser.
• A Computational Introduction to Number Theory and Algebra. Full online version of a printed book on computational number theory, generously made freely available by its author Victor Shoup and the publisher Cambridge University Press.
• Codes, Ciphers and Codebreaking. Historical account of cryptography by Greg Goebel. He is not a professional cryptographer, but in particular the historical account in his book is interesting.

Books

Links

Most Important Facts

• Alice and Bob, and Eve.

Classic Ciphers

• Cipher
• Shift Cipher
• Substitution Cipher
• Affine Cipher
• Vigenère Cipher
• Hill Cipher
• Permutation Cipher

Classic Cryptanalysis

• Frequency Analysis
• Letter Frequencies
• Bigram, Trigram, . . ., N-gram
• Dot Product and Inner Product
• Kasisiski Test
• Index of Coincidence

Perfect Secrecy and Information Theory

• Bayes' Theorem
• Perfect Secrecy
• Entropy
• Concavity
• Jensen's Inequality
• Kraft's Inequality
• Shannon's Source Coding Theorem
• Huffman Coding
• Unicity Distance
• A Mathematical Theory of Communication, Shannon, 1948. One of the most influential papers ever written.
• Communication Theory of Secrecy Systems, Shannon, 1949.
• Rényi Entropy
• Min Entropy
• Leftover Hash Lemma

Modern Ciphers

• Kerckhoffs' Principle
• Substitution-Permutation Network
• A Tutorial on Linear and Differential Cryptanalysis, Heys. The treatment in Stinson's book is based on this paper.
• DES
• Standing the Test of Time: The Data Encryption Standard
• Triple-DES
• DES-X
• How to protect DES against exhaustive key search, Kilian and Rogaway, Crypto 96.
• The Security of DESX, Rogaway. A short note giving a high level description of why we expect DESX to be more secure than DES.
• Linear Cryptanalysis of DES, Junod. Describes findings of an actual implementation of linear cryptanalysis of DES.
• Modes of Operations
• NIST Recommendation for Block Cipher Modes of Operation, 2001.

Probability Theory

• Birthday Paradox

Elementary Number Theory

• Extended Euclidean Algorithm
• Bezout's Lemma
• Chinese Remainder Theorem
• Coset
• Lagrange Theorem
• Euler's Phi Function
• Fermat's Little Theorem
• Euler's Theorem
• Modular Multiplicative Group of Integers
• Finite Field
• Quadratic Residue
• Jacobi Symbol
• Prime Number Theorem
• Solovay-Strassen Primality Test
• Integer Factorization
• Discrete Logarithm

Public Key Cryptosystems

• Public-Key Cryptography
• Merkle's Puzzles
• The RSA Problem, Rivest and Kaliski. A paper giving an overview of the history of the RSA problem.
• RSA/Rabin least significant bits are 1/2+1/poly(log N) secure, Chor and Goldreich.
• Rabin's Cryptosystem
• Key Exchange
• Diffie-Hellman Key Exchange.

Random Oracle Model

• How To Prove Yourself: Practical Solutions to Identification and Signature Problems, Fiat and Shamir, 1987. Paper that, among other important contributions, suggest the heuristic of considering a hash function as if it was random.
• Random oracles are practical: A paradigm for designing efficient protocols, Bellare and Rogaway, 1993. Proposing the random oracle model as a general practical tool to construct efficient cryptographic schemes.
• The Random Oracle Methodology, Revisited, Canetti, Goldreich, and Halevi, 1998. First paper proving that the random oracle methodology is unsound.
• Indifferentiability, Impossibility Results on Reductions, and Applications to the Random Oracle Methodology, Maurer, Renner, and Holenstein. Especially the first part of this paper gives a simple explaination of the key issue with random oracles.

Hashfunctions

• Hashfunction
• Merkle-Damgård
• Universal Hashing
• CBC-MAC

Pseudo-Random Generators

• Hardware Random Number Generator
• Pseudo-Random Generator
• /dev/random
• Analysis of the Linux Random Number Generator, Zvi Gutterman, Benny Pinkas, and Tzachy Reinman.
• Yarrow
• Fortuna
• Attacks Against Weak PRGs